Not quite sure what this is actually asking :(

[chickenpop]

No idea what it's asking, let alone how to work it out 

Given:
w= 1+ ai
|w^3| = (1 +a^2)^(3/2)

Let p(z)=z^3 + bz^2 +cz + d where b,c and d are non-zero real constants. If p(z) =0 for z=w and all roots of p(z)=0 satisfy |z^3| =8, find the values of b,c and d and show that these are the only possible values

[TrueTears]

Use the information 1+ai is a solution to P(z) to find it's other roots (Hint: the coefficients are all non-zero real constant, so think of the complement of 1+ai). Then plug them into |z^3|=8 to work out the value of the constant.

I'm guessing this is VCAA 2008 paper? I rmb doing this Q lol

[jasoN-]

Yeah it's a VCAA question, it also gives u , giving you
when

as :
and are factors
Multiply the factors together:
  [DOTS]

is a factor

Now you're also given
Therefore
and hence
This gives you two possible factors or

This looks correct as b,c and d are all non-zero Real constants.
However you can't disregard the other factor ()
So using as a factor:


This cannot be a factor as it implies b and c are zero constants.

Therefore b=-4,c=8, d=-8

[98.40_for_sure]

Heh, i got stuck on this question last week, wasn't sure whether to use (z-2) or (z+2)

[Courante]

JACKS!! xD

[98.40_for_sure]

JACKS!! xD

Hahahah jacks didn't explain it very well though...

[letsride]

yea this was done at jacks
imo he rushed it, not his best work.

[darkphoenix]

LOL yeah jacks. True he does rush quite alot.

[98.40_for_sure]

He frickin just left the question mid-way... people's parents can wait, i wanted to know the solution -_-

[darkphoenix]

What? really? He finished off the question for us then left question 3 for next week.